Weak gravity and other Math B oddities

#7 The height of a swimmer’s dive off a 10-foot platform into a diving pool is modeled by the equation , where x represents the number of seconds since the swimmer left the diving board and y represents the number of feet above or below the water’s surface. What is the farthest depth below the water’s surface that the swimmer will reach?

Physics or sports folks out there – how horrible is that model? I assume that when the diver hits the water, the acceleration changes dramatically, right? And for the part before the water an acceleration of 4ft/s per s is more like moon gravity than Albany gravity (even though I hear there is strange stuff up there). Can anyone supply more detail?

Also note the subtle error in the description of y.

(for kiddies: answer is the vertex of the parabola – (3,-8) so 8 feet below the water’s surface.)

#30 [ corrected the wrong #: #8] Farmington, New York, has plans for a new triangular battlefield park. If plotted on a coordinate grid, the vertices would be A(3,3), B(5,-2), and C(-3,-1). However an evil wizard a tract of land has has seized control become available that would enable and the wizard the planners to plans to turn it into a strip mall increase the size of the park, which is based on the following transformation of the original triangular battlefield park,

my version would at least make it amusing. Theirs is stupid.

they treat their notation as standard (not requiring explanation). I have seen enough transformational geometry texts to know that it is not. having New York State official (but not accepted by the wide world) mathematical nomenclature is unacceptable.

they don’t specify the center of dilation. they don’t specify the center of rotation.

this question fails to assess something that matters: whether kids understand how to compose. If they do the rotation first, no problem… (although, in defense of Albany, there is a multiple choice item, #9, that did exactly that, and with the trap answer.)

kiddies, they meant the center of each transformation to be at the origin, and we work from do the first to the second, iow, the dilation comes first:

and the coordinates become (6,6), (-4,-10), (-2,6).

#10 A central angle of a circular garden measures 2.5 radians and intercepts an arc of 20 feet. What is the radius of the garden?

Stop right there! We don’t measure angles on the ground in radians. When we do use radians, they appear as multiples of π!

“Also note the subtle error in the description of y.” The only thing I notice is that y should be the location of the sole of the diver’s foot at time x, with respect to water’s surface (since its a 10 ft board, so at x=0 it is the sole on the board, whereas for diving depth you probably wouldn’t measure to the sole of the foot (the highest point, once the diver is in … My guess is you had something else in mind. What?